急若cos(α-β)=√5/5cos2α=√10/10,且α,β均为锐角,且α

Question

急 若cos(α-β)=√5/5 cos2α=√10/10 ,且α,β均为锐角,且α

Answer 1

sin(a-β)=-2√5/5 sin2a=3√10/10
cos(α+β)
=cos[-(a+β)]
=cos(-α-β)
=cos(α-β-2a)
=cos(α-β)cos2a+sin(α-β)sin2a
=√5/5x√10/10-2√5/5x3√10/10
=-√2/2
α+β=arccos(-√2/2)=135°